Solving and answering arithmetic and algebraic problems using natural language processing

ABSTRACT

A method for solving and answering an arithmetic or algebraic problem using natural language processing (NLP) is provided. The method may include receiving an input statement associated with the arithmetic or algebraic problem. The method may also include determining whether each sentence within a plurality of sentences associated with the input statement is a well-formed sentence from a mathematical perspective. The method may further include converting each statement into a well-formed sentence based on the determining whether each sentence within a plurality of sentences associated with the input statement is a well-formed sentence from a mathematical perspective. Additionally, the method may include converting each well-formed sentence into a mathematical equation to form a set of equations. Also, the method may include solving the set of equations to compute a mathematical result. The method may include narrating the mathematical result in natural language.

CROSS REFERENCE

The present application is a continuation of and claims priority under35 U.S.C. §120 of U.S. patent application Ser. No. 14/306,267 filed onJun. 17, 2014, which is incorporated by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates generally to the field of computing, andmore particularly to solving arithmetic and algebraic problems.

BACKGROUND

There are several types of arithmetic and algebraic problems which aretypically described in natural language through a number of factoidsentences and one or more questions. The questions may be interrogativequeries, such as Who, What, How many, etc. The arithmetic and algebraicproblems may also be described through deterministic words such as “Findthe number of . . . ”. Such arithmetic and algebraic problems typicallydepend on people (e.g., tutors or teachers) to solve the word problemsposed by students or users. Additionally, such arithmetic and algebraicproblems may also be solved via “interactive” screens which usepre-computed logic and value or provide textual explanation to apre-specified math problem. Furthermore, a video may be utilized where aperson or tutor explains the logic and the solution to a pre-specifiedmath problem.

SUMMARY

According to one embodiment, a method for solving and answering anarithmetic or algebraic problem using natural language processing (NLP)is provided. The method may include receiving an input statementassociated with the arithmetic or algebraic problem. The method may alsoinclude determining whether each sentence within a plurality ofsentences associated with the input statement is a well-formed sentencefrom a mathematical perspective. The method may further includeconverting each statement into a well-formed sentence based on thedetermining whether each sentence within a plurality of sentencesassociated with the input statement is a well-formed sentence from amathematical perspective. Additionally, the method may includeconverting each well-formed sentence into a mathematical equation toform a set of equations. Also, the method may include solving the set ofequations to compute a mathematical result. The method may includenarrating the mathematical result in natural language.

According to another embodiment, a computer system for solving andanswering an arithmetic or algebraic problem using natural languageprocessing (NLP) is provided. The computer system may include one ormore processors, one or more computer-readable memories, one or morecomputer-readable tangible storage devices, and program instructionsstored on at least one of the one or more storage devices for executionby at least one of the one or more processors via at least one of theone or more memories, wherein the computer system is capable ofperforming a method. The method may include receiving an input statementassociated with the arithmetic or algebraic problem. The method may alsoinclude determining whether each sentence within a plurality ofsentences associated with the input statement is a well-formed sentencefrom a mathematical perspective. The method may further includeconverting each statement into a well-formed sentence based on thedetermining whether each sentence within a plurality of sentencesassociated with the input statement is a well-formed sentence from amathematical perspective. Additionally, the method may includeconverting each well-formed sentence into a mathematical equation toform a set of equations. Also, the method may include solving the set ofequations to compute a mathematical result. The method may includenarrating the mathematical result in natural language.

According to yet another embodiment, a computer program product forsolving and answering an arithmetic or algebraic problem using naturallanguage processing (NLP) is provided. The computer program product mayinclude one or more computer-readable storage devices and programinstructions stored on at least one of the one or more tangible storagedevices, the program instructions executable by a processor. Thecomputer program product may also include program instructions toretrieve an input statement associated with the arithmetic or algebraicproblem. The computer program product may also include programinstructions to determine whether each sentence within a plurality ofsentences associated with the input statement is a well-formed sentencefrom a mathematical perspective. The computer program product mayfurther include program instructions to convert each statement into awell-formed sentence based on the determining whether each sentencewithin a plurality of sentences associated with the input statement is awell-formed sentence from a mathematical perspective. Additionally, thecomputer program product may include program instructions to converteach well-formed sentence into a mathematical equation to form a set ofequations. Also, the computer program product may include programinstructions to solve the set of equations to compute a mathematicalresult. The computer program product may include program instructions tonarrate the mathematical result in natural language.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

These and other objects, features and advantages of the presentinvention will become apparent from the following detailed descriptionof illustrative embodiments thereof, which is to be read in connectionwith the accompanying drawings. The various features of the drawings arenot to scale as the illustrations are for clarity in facilitating oneskilled in the art in understanding the invention in conjunction withthe detailed description. In the drawings:

FIG. 1 illustrates a networked computer environment according to oneembodiment;

FIG. 2 illustrates an exemplary dictionary containing a mapping of verbsand mathematical operators according to one embodiment;

FIGS. 3A-3B is an operational flowchart illustrating an overallalgorithm for answering arithmetic and algebraic problems using naturallanguage according to one embodiment;

FIGS. 4A-4B is an operational flowchart illustrating an algorithm tocheck if a sentence is well-formed from a mathematical perspectiveaccording to one embodiment;

FIGS. 5A-5B is an operational flowchart illustrating an algorithm toconvert a source sentence into a well-formed sentence (i.e., a targetsentence) according to one embodiment;

FIGS. 6A-6B is an operational flowchart illustrating an algorithm toconvert a well-formed sentence into a mathematical equation according toone embodiment;

FIG. 7 is an operational flowchart illustrating an algorithm to solve aset of mathematical equations and return a result according to oneembodiment;

FIG. 8 is an operational flowchart illustrating an algorithm to narratethe mathematical equations in natural language according to oneembodiment;

FIGS. 9A-9B illustrate examples solving a math problem using thedescribed algorithms in FIGS. 3-8 according to one embodiment;

FIG. 10 is a block diagram of internal and external components ofcomputers and servers depicted in FIG. 1 according to at least oneembodiment.

DETAILED DESCRIPTION

Detailed embodiments of the claimed structures and methods are disclosedherein; however, it can be understood that the disclosed embodiments aremerely illustrative of the claimed structures and methods that may beembodied in various forms. This invention may, however, be embodied inmany different forms and should not be construed as limited to theexemplary embodiments set forth herein. Rather, these exemplaryembodiments are provided so that this disclosure will be thorough andcomplete and will fully convey the scope of this invention to thoseskilled in the art. In the description, details of well-known featuresand techniques may be omitted to avoid unnecessarily obscuring thepresented embodiments.

Embodiments of the present invention relate generally to the field ofcomputing, and more particularly to solving arithmetic and algebraicproblems. The following described exemplary embodiments provide asystem, method and program product for solving arithmetic and algebraicproblems using natural language processing (NLP).

As previously explained, there are several types of arithmetic andalgebraic problems which are typically described in natural languagethrough a number of factoid sentences and one or more questions. Sucharithmetic and algebraic problems typically depend on people to solvethe word problems posed by students or users. Additionally, sucharithmetic and algebraic problems may also be solved via “interactive”screens or a video where a person or tutor explains the logic and thesolution to a pre-specified math problem. Additionally, a calculatortool may be utilized if a basic arithmetic equation, such as (2+2) isentered in the search bar. However, currently there are no existingsolutions or computer applications or systems which can automaticallysolve such arithmetic or algebraic math problems in real-time usingnatural language processing (NLP). Therefore, it may be advantageous,among other things, to solve arithmetic or algebraic math problemsthrough a question-answer system which may understand natural languageas well as provide natural language answers. As such, the presentembodiment may allow a user to enter a math problem in natural languageand the user may receive an automatic interactive response or solutionfrom the computer in real-time.

According to at least one embodiment, a computer-based question-answersystem may understand an arithmetic or algebraic math problem stated innatural language and provide an answer or solution in real-time as anatural language answer. One implementation of the present embodimentmay receive an input problem statement and question to be answered (froma data source or user interface) and determine whether the originalsentences are well-formed from a mathematical perspective. Then, ifrequired, the method may convert the input sentences to a sequence ofsentences which are well-formed from a mathematical perspective andconvert the well-formed sentences into mathematical equations. Thepresent embodiment may also solve the set of equations using applicablelogic or mathematical methods to get a mathematical result. The presentembodiment may also correlate the mathematical result to the originalquestion to be answered and then narrate the mathematical result innatural language, as an answer to the original question.

Additionally, according to at least one implementation, the presentembodiment may also include a dictionary which may contain a mappingbetween verbs or action words and mathematical operators, such that foreach verb or action word, the effect of the mathematical operator on theoperands (subject(s) and the object(s) of a sentence) may be specifiedin the dictionary. This dictionary may be created, updated, and/ormaintained as a separate entity.

Also, the present embodiment may be generic and may be used by acomputer-based question-answer system to solve a diverse set ofarithmetic or algebraic mathematical problems in natural language and inreal-time. Furthermore, the present embodiment may be used for anynatural language supported by natural language processing algorithms.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The following described exemplary embodiments provide a system, methodand program product for solving arithmetic and algebraic problems usingnatural language processing (NLP). As previously described, there may bedifferent types of arithmetic or algebraic mathematical problems whichmay be stated in natural language. Such “math problem statements” may becommonly used in academia and text books as an aid to teachingmathematical concepts and provide practical exposure to students andreaders through “student exercises”. The problem statements may also beused to describe practical problems encountered in industry. Examples ofsuch math problems include, but are not limited to the following:

Age Problems usually compare the ages of people. They may involve asingle person, comparing his/her age in the past, present or future.They may also compare the ages involving more than one person.

-   -   Average Problems involve the computations for arithmetic mean,        weighted average of different quantities, average speed        computation, etc.    -   Coin/Stamp/Ticket Problems deal with items with denominated        values.    -   Consecutive Integer Problems deal with consecutive numbers. The        number sequences may be Even or Odd, or some other simple number        sequences.    -   Digit Problems involve the relationship and manipulation of        digits in numbers.    -   Distance Problems involve the calculation of distance an object        travels given the total time, or the travel rate over a period        of time, including objects that Travel at Different Rates or        objects that Travel in Different Directions, etc.    -   Fraction Problems involve fractions or parts of a whole.    -   Geometry Word Problems deal with geometric figures and angles        described in words, including word problems Involving        Perimeters, Involving Areas and Involving Angles.    -   Integer Problems involve numerical representations of word        problems, involving 1 unknown, 2 unknowns or more than 2        unknowns.    -   Interest Problems involve calculations of simple interest.    -   Lever Problems deal with the lever principle described in word        problems, involving 2 or more objects.    -   Mixture Problems involve items or quantities of different values        that are mixed together. This involve Adding to a Solution,        Removing from a Solution, Replacing a Solution, or Mixing Items        of Different Values.    -   Motion Word Problems are word problems that use the distance,        rate and time formula.    -   Number Sequence Problems use number sequences in the        construction of word problems, including finding the value of a        particular term or the pattern of a sequence, etc.    -   Proportion Problems involve proportional and inversely        proportional relationships of various quantities.    -   Ratio Problems require relating quantities of different items in        certain known ratios, or work out the ratios given certain        quantities. This could be Two-Term Ratios or Three-Term Ratios,        etc.    -   Variation Word Problems may consist of Direct Variation        Problems, Inverse Variation Problems or Joint Variation        Problems.    -   Work Problems involve different people doing work together at        different rates such as Two Persons, More Than Two Persons or        Pipes Filling up a Tank, etc.

Additionally, implementations of the present embodiment may includeutilizing existing technology, including, but not limited to thefollowing:

-   -   Parsing/Syntactic Analysis: Parsing or Syntactic Analysis is the        process of analyzing a string of symbols, either in natural        language or in computer languages, according to the rules of a        formal grammar. For example, Stanford        Parser—http://nlp.stanford.edu:8080/parser/ or Carnegie Mellon        University Parser:        http://www.link.cs.cmu.edu/link/submit-sentence-4.html.    -   POS Tagging: In corpus linguistics, Part-Of-Speech Tagging (POS        tagging or POST), also called grammatical tagging, is the        process of marking up a word in a text (corpus) as corresponding        to a particular part of speech, based on both its definition, as        well as its context—i.e. relationship with adjacent and related        words in a phrase, sentence, or paragraph. For example,        University of Pennsylvania—Penn Tree Bank:        http://www.cis.upenn.edu/˜treebank/.    -   Typed Dependency Analysis: A representation of grammatical        relations between words in a sentence. They have been designed        to be easily understood and effectively used by people who want        to extract textual relations. In general, dependencies are        triplets: name of the relation, governor and dependent. For        example, The Stanford Natural Language Processing Group—Typed        Dependencies:        http://nlp.stanford.edu/software/stanforddependencies.shtml.    -   Structural/Syntactic Ambiguity: Syntactic ambiguity is a        property of sentences which may be reasonably interpreted in        more than one way, or reasonably interpreted to mean more than        one thing. Ambiguity may or may not involve one word having two        parts of speech or homonyms. Syntactic ambiguity arises not from        the range of meanings of single words, but from the relationship        between the words and clauses of a sentence, and the sentence        structure implied thereby. When a reader can reasonably        interpret the same sentence as having more than one possible        structure, the text is equivocal and meets the definition of        syntactic ambiguity. For example, Linguistics Online—Syntactic        Ambiguity:        http://languagelink.let.uu.nl/˜lion/?s=Grammar_exercises/grammar_4.    -   Anaphora Resolution: In linguistics, an anaphora is a type of        expression whose reference depends upon another referential        element. It is co-referential with the expression in subject        position. An anaphoric expression is represented by a pro-form        or some other kind of deictic, for instance, a pronoun referring        to its antecedent. For example, Cornell University—Anaphora:        http://www.cs.cornell.edu/boom/2000sp/2000%20projects/anaphora/definition.html.    -   Morphological Analysis: In linguistics, morphology is the        identification, analysis and description of the structure of a        given language's morphemes and other linguistic units, such as        root words, affixes, parts of speech, intonation/stress, or        implied context (words in a lexicon are the subject matter of        lexicology). Morphological typology represents a method for        classifying languages according to the ways by which morphemes        are used in a language. For example, Wikipedia:        http://en.wikipedia.org/wiki/Morphological_analysis.

Referring now to FIG. 1, an exemplary networked computer environment 100in accordance with one embodiment is depicted. The networked computerenvironment 100 may include a computer 102 with a processor 104 and adata storage device 106 that is enabled to run an Arithmetic andAlgebraic Problem Solving Program 108A. The networked computerenvironment 100 may also include a server 112 that is enabled to run anArithmetic and Algebraic Problem Solving Program 108B and acommunication network 110. The networked computer environment 100 mayinclude a plurality of computers 102 and servers 112, only one of whichis shown for illustrative brevity. The communication network may includevarious types of communication networks, such as a wide area network(WAN), local area network (LAN), a telecommunication network, a wirelessnetwork, a public switched network and/or a satellite network. Thenetwork computer environment may also include a dictionary 114 which maycontain a mapping between verbs or action words and mathematicaloperators, such that for each verb or action word, the effect of themathematical operator on the operands (subject(s) and the object(s) of asentence) may be specified in the dictionary. According to at least oneimplementation, the dictionary 114 may be created, updated, andmaintained as a separate entity. It may be appreciated that FIG. 1provides only an illustration of one implementation and does not implyany limitations with regard to the environments in which differentembodiments may be implemented. Many modifications to the depictedenvironments may be made based on design and implementationrequirements.

The client computer 102 may communicate with server computer 112 via thecommunications network 110. The communications network 110 may includeconnections, such as wire, wireless communication links, or fiber opticcables. As will be discussed with reference to FIG. 10, server computer112 may include internal components 800 a and external components 900 a,respectively and client computer 102 may include internal components 800b and external components 900 b, respectively. Client computer 102 maybe, for example, a mobile device, a telephone, a personal digitalassistant, a netbook, a laptop computer, a tablet computer, a desktopcomputer, or any type of computing device capable of running a programand accessing a network.

A program, such as an Arithmetic and Algebraic Problem Solving Program108A and 108B may run on the client computer 102 or on the servercomputer 112. The Arithmetic and Algebraic Problem Solving Program 108A,108B may be utilized to solve arithmetic and algebraic problems. Forexample, a user using an Arithmetic and Algebraic Problem SolvingProgram 108A, running on a client computer 102, may connect via acommunication network 110 to server computer 112, which may also berunning an Arithmetic and Algebraic Problem Solving Program 108B.Furthermore, the user using client computer 102 or server 112 mayutilize the Arithmetic and Algebraic Problem Solving Program 108A, 108Bto solve a diverse set of arithmetic or algebraic mathematical problemsin natural language and in real-time. The Arithmetic and AlgebraicProblem Solving is explained in further detail below with respect toFIGS. 3-8.

Referring now to FIG. 2, an exemplary dictionary 200 containing amapping of verbs and mathematical operators in accordance with oneembodiment is depicted. According to at least one implementation, thepresent embodiment may include a dictionary 114 containing a mappingbetween verbs 202 or action words 202 and mathematical operators 204. Assuch, for each verb 202 or action word 202, the effect of themathematical operator 204 on the operands (subject(s) 206 and theobject(s) 208) may be specified in the dictionary 114. Typically,coefficients or numerals 210 in a sentence act as multipliers with theobject(s) 208 or subject(s) 206 to which they refer. This may depend onthe context, and may be determined through natural language processing(NLP) parsing and determination of typed dependencies.

A sample mapping of certain verbs 202 and typical mathematical operators204, such as “add”, “subtract”, “multiply”, “divide”, “equals” (e.g., (+− * / =)) is illustrated in FIG. 2 and may be included in the dictionary114. According to the present embodiment, the mapping may be used in ageneric way to resolve how an operator 204 may operate on a subject 206or object 208 in a given sentence containing a specific verb or actionword.

Referring now to FIGS. 3A-3B, an operational flowchart 300 illustratingan overall algorithm (i.e., algorithm #1) for answering arithmetic andalgebraic problems using natural language in accordance with oneembodiment is depicted. At 302, the method may get the input problemstatement and question to be answered from a data source or userinterface. For example, an input statement may be a statement such as,(“Ashish had 2 apples. He gave one to Joy. How many are left?”).

Then at 304, the sequence of sentences in the input statement may bechecked. As such, the sequence of the sentences of the input statementmay be examined to determine the order of the sentences. Next at 306, itis determined whether the question or query to be answered is the lastsentence in the sequence. If at 306, it is determined that the questionor query to be answered is not the last sentence in the sequence, thenat 308, the method may re-sequence the sentences so that the sentencewith the question or query is the last sentence in the sequence. Thenthe method may continue back to step 304 (previously explained) to checkthe sequence of sentences in the input.

However, if at 306, it is determined that the question or query to beanswered is the last sentence in the sequence, then at 310, for eachsentence (Sx) in the input, the method may perform steps 312-324described below.

At 312, it is determined whether the sentence is well-formed from amathematical perspective. As such, according to one implementation, themethod may base the determination as to whether the sentence iswell-formed formed from a mathematical perspective, on algorithm #2 (400(FIG. 4)) explained in detail below.

If at 312, it is determined that the sentence is not well-formed from amathematical perspective, then at 314, the method may convert the inputsentence (Sx) into a well-formed sentence from a mathematicalperspective. As such, according to one implementation, the method mayconvert the input sentence (Sx) into a well-formed sentence from amathematical perspective by utilizing algorithm #3 (500 (FIG. 5))explained in detail below. Then the method may continue to step 316 toconvert the well-formed sentence (Sx) into a mathematical equation.

However, if at 312, it is determined that the sentence is well-formedfrom a mathematical perspective, then at 316 the method may convert thewell-formed sentence (Sx) into a mathematical equation. According to oneimplementation, the method may convert the well-formed sentence (Sx)into a mathematical equation by utilizing algorithm #4 (600 (FIG. 6))explained in detail below and by referring to the (Dictionary #1) 114which maps verbs and math operators.

Then at 318, it is determined whether there are any more sentences toevaluate. If at 318 it is determined that there are more sentences toevaluate, then the method may continue back to step 310 previouslydescribed.

However, if at 318 it is determined that there are not any moresentences to evaluate, then at 320 the method may solve the set ofequations to compute a mathematical result. According to oneimplementation the method may refer to the (Dictionary #1) 114 which maymap verbs and math operators. Additionally, the method may receive theset of equations from the (Transient Repository #2) 326 which is therepository of equations for a given set of sentences (Sx). Furthermore,the method may solve the set of equations to compute a mathematicalresult by utilizing algorithm #5 (700 (FIG. 7)) explained in detailbelow.

Next at 322, the mathematical result is narrated in natural language asan answer to the original question. According to one implementation, themethod may utilizing algorithm #6 (800 (FIG. 8)) explained in detailbelow to narrate the mathematical result in natural language as ananswer to the original question. Then at 324, the method may output thenarrated answer in natural language. For example, a narrated answer innatural language may be an answer such as, (“Ashish has 1 apple left”).

Referring now to FIGS. 4A-4B, an operational flowchart 400 illustratingan algorithm (i.e., algorithm #2) to check if a sentence is well-formedfrom a mathematical perspective in accordance with one embodiment isdepicted. For example, a well-formed sentence may be a sentence such as,(“Ashish had 2 apples. Ashish gave 1 apple to Joy. How many apples areleft with Ashish?”).

At 402, the method may get the source sentence as input to a naturallanguage processing (NLP) parser. Then at 404, part-of-speech (POS)tagging is performed on the source sentence. As described above, incorpus linguistics, part-of-speech Tagging (POS tagging or POST), alsocalled grammatical tagging, is the process of marking up a word in atext (corpus) as corresponding to a particular part of speech, based onboth its definition, as well as its context (i.e., relationship) withadjacent and related words in a phrase, sentence, or paragraph.

Next, at 406, parsing and parse tree generation are performed. Aspreviously described, parsing or syntactic analysis is the process ofanalyzing a string of symbols, either in natural language or in computerlanguages, according to the rules of a formal grammar. Then at 408,typed dependencies are determined. As described above, the typeddependencies are a representation of grammatical relations between wordsin a sentence.

Next at 410, the method may perform check 1 to determine whether thesentence requires anaphora resolution. As previously explained, ananaphora is a type of expression whose reference depends upon anotherreferential element. If at 410 it is determined that the sentence doesrequire anaphora resolution, then the method may continue to step 420where it is determined that the sentence is not well-formed. However, ifat 410 it is determined that the sentence does not require anaphoraresolution, then the method may continue to step 412.

Then at 412, the method may perform check 2 to determine whether thesentence requires structural disambiguation. As previously explained,when a reader can reasonably interpret the same sentence as having morethan one possible structure, the text is equivocal and meets thedefinition of syntactic ambiguity. If at 412 it is determined that thesentence does requires structural disambiguation, then the method maycontinue to step 420 where it is determined that the sentence is notwell-formed. However, if at 412 it is determined that the sentence doesnot require structural disambiguation, then the method may continue tostep 414.

Next, at 414, the method may perform check 3 to determine whether thesentence requires morphological analysis. As previously explained,morphology is the identification, analysis and description of thestructure of a given language's morphemes and other linguistic units,such as root words, affixes, parts of speech, intonation or stress, orimplied context. If at 414 it is determined that the sentence doesrequire morphological analysis, then the method may continue to step 420where it is determined that the sentence is not well-formed. However, ifat 414 it is determined that the sentence does not require morphologicalanalysis, then the method may continue to step 416.

Then at 416, the method may perform check 4 to determine whether thesentence requires converting numerical text to numerals. If at 416 it isdetermined that the sentence does require converting numerical text tonumerals, then the method may continue to step 420 where it isdetermined that the sentence is not well-formed. However, if at 416 itis determined that the sentence does not require converting numericaltext to numerals, then the method may continue to step 418.

Then at 418, the method may perform check 5 to determine whether thesentence requires any other corrections. If at 418 it is determined thatthe sentence does require other corrections, then the method maycontinue to step 420 where it is determined that the sentence is notwell-formed. However, if at 418 it is determined that the sentence doesnot require any other corrections, then the method may determine at step422 that the sentence is well formed, and the method may end.

Referring now to FIGS. 5A-5B, an operational flowchart 500 illustratingan algorithm (i.e., algorithm #3) to convert a source sentence into awell-formed sentence (i.e., a target sentence) in accordance with oneembodiment is depicted. At 502, the method may get the source sentenceas input to a natural language processing (NLP) parser.

Then at 504, part-of-speech (POS) tagging (of the source sentence) isperformed. As previously described, in corpus linguistics,part-of-speech Tagging (POS tagging or POST), also called grammaticaltagging, is the process of marking up a word in a text (corpus) ascorresponding to a particular part of speech, based on both itsdefinition, as well as its context—i.e. relationship with adjacent andrelated words in a phrase, sentence, or paragraph.

Next at 506, parsing and parse tree generation (of the source sentence)are performed. As previously described, parsing or syntactic analysis isthe process of analyzing a string of symbols, either in natural languageor in computer languages, according to the rules of a formal grammar.Then at 508, typed dependencies (for the source sentence) aredetermined. As previously explained, the typed dependencies are arepresentation of grammatical relations between words in a sentence.

Next at 510, anaphora are resolved. As previously explained, an anaphorais a type of expression whose reference depends upon another referentialelement. Then at 512, structural disambiguation is performed. Aspreviously explained, when a reader can reasonably interpret the samesentence as having more than one possible structure, the text isequivocal and meets the definition of syntactic ambiguity.

Next at 514, it is determined whether user input is required to resolvethe ambiguity. If at 514 it is determined that user input is required toresolve the ambiguity, then at 516, the method may get the user inputand continue back to step 512 to perform the structural disambiguation.However, if at 514, it is determined that user input is not required toresolve the ambiguity, then at 518, the method may convert numericaltext into numerals. For example, the method may convert numerical text,such as “two” into the numeral “2”.

Then at 520, morphological analysis and correction may be performed. Aspreviously explained, morphology is the identification, analysis anddescription of the structure of a given language's morphemes and otherlinguistic units, such as root words, affixes, parts of speech,intonation or stress, or implied context. According to oneimplementation of the present embodiment, the morphological analysis andcorrection may be performed by referring to the Dictionary #2 (526)which is the language dictionary and thesaurus repository.

Next at 522, any other grammatical or semantic corrections to the sourcesentence may be performed. Then at 524, the method may determine thetarget sentence (from the source sentence and all necessarysubstitutions) as a well-formed and well-formatted sentence.

Referring now to FIGS. 6A-6B, an operational flowchart 600 illustratingan algorithm (i.e., algorithm #4) to convert a well-formed sentence intoa mathematical equation in accordance with one embodiment is depicted.At 602, the method may get the well-formed sentence as an input to anatural language processing (NLP) parser. According to oneimplementation, the well-formed sentence may be the “current sentence”or the output form algorithm #3 previously described with respect toFIGS. 5A-5B.

Then at 604, the method may perform par-of-speech (POS) tagging of thecurrent sentence. As previously described, in corpus linguistics,part-of-speech Tagging (POS tagging or POST), also called grammaticaltagging, is the process of marking up a word in a text (corpus) ascorresponding to a particular part of speech, based on both itsdefinition, as well as its context (i.e., relationship) with adjacentand related words in a phrase, sentence, or paragraph.

Next at 606, the method may perform parsing and parse tree generation ofthe current sentence. As previously described, parsing or syntacticanalysis is the process of analyzing a string of symbols, either innatural language or in computer languages, according to the rules of aformal grammar.

Then at 608 typed dependencies may be determined for the currentsentence. As previously explained, the typed dependencies are arepresentation of grammatical relations between words in a sentence.

Next at 610, the subject(s), object(s), verb(s), action(s), numeral(s),etc. are determined for the current sentence from the typeddependencies. As previously explained, the typed dependencies are arepresentation of grammatical relations between words in a sentence.

Then at 612, it is determined whether the variables are alreadyassociated with specific subjects or objects of the current sentence,from previous sentences in this set. According to one implementation thedetermination as to whether the variables are already associated withspecific subjects or objects of the current sentence, from previoussentences in this set may be made by reading the Transient Repository #1(614) which is a repository of mapping of subjects or objects tovariable names for a given set of sentences (Sx).

If at 612 it is determined that the variables are not already associatedwith specific subjects or objects of the current sentence, from previoussentences in this set, then the method may continue to step 618 toassign new variable names to the remaining subject(s) and/or object(s)in the current sentence. However, if at 612 it is determined that thevariables are already associated with specific subjects or objects ofthe current sentence, from previous sentences in this set, then at 616,the method may assign existing variable names to the respectivesubject(s) and/or object(s) in the current sentence.

Next at 618, new variable names are assigned to the remaining subject(s)and/or object(s) in the current sentence. Then at 620, the method maycreate or update the mapping of the variable name(s) and subject(s) orobject(s) in the current sentence to a Transient Repository #1 (614)which is a repository of mapping of subjects or objects to variablenames for a given set of sentences (Sx).

Next at 622, the mathematical operator(s) are determined based on theverb(s), action(s), or numeral(s) in the current sentence. According toone implementation, the determination of the mathematical operator(s)may be made by referring to a Dictionary #1 (114) which maps verbs andmath operators.

Then at 624, the mathematical equation for the current sentence (fromthe variables and mathematical operators) is formulated. Next at 626,the method may create or update the mathematical equation for thecurrent sentence to a Transient Repository #2 (326) which is therepository of equations for a given set of sentences (Sx).

Referring now to FIG. 7, an operational flowchart 700 illustrating analgorithm (i.e., algorithm #5) to solve a set of mathematical equationsand return a result in accordance with one embodiment is depicted.

At 702, the method may get the set of all mathematical equations (i.e.,“input equations”) for the given set of sentences (Sx) which is theoutput from algorithm #4 (FIGS. 6A-6B) previously described. Accordingto one implementation, the method may get the set of all mathematicalequations (i.e., “input equations”) for the given set of sentences (Sx)from a Transient Repository #2 (326) which is the repository ofequations for a given set of sentences (Sx).

Then at 704, the method may solve or resolve the set of “inputequations” to a final set of equations (“target equations”) Tx, suchthat each of the target equations is unique and exclusive from othertarget equations in the set Tx and the set of equations Tx cannot beresolved further in terms of its constituent variables. According to thepresent embodiment, step 704 may be a generic step and as such, theremay be many possible ways to implement this step regarding the solvingof equations. For example, one implementation to perform the stepregarding the solving of equations may be as follows:

(a) Take each “pair” of equations [A & B].

(b) Resolve all variables and mathematical operations for the given pairA & B to get a resultant equation C.

(c) Take resultant equation C and the next available equation X; ResolveC and X to get another resultant equation D; and so on until all theequations in the set of “input equations” are resolved to get the finalset of target equation(s) Tx which cannot be resolved further in termsof variables.

Next at 706, the method may determine the variable present in theoriginal question to be answered. According to one implementation, themethod may determine the variable present in the original question to beanswered by reading the Transient Repository #1 (614) which is arepository of mapping of subjects or objects to variable names for agiven set of sentences (Sx).

Then at 708, the method may determine the target equations Tz whichcontain the variables present in the original question to be answered(Tz may be a sub-set of Tx). Next at 710, the method may determine thefinal values for each of the variables contained in the target equationsTz, as the Mathematical Result TR (712).

Referring now to FIG. 8, an operational flowchart 800 illustrating analgorithm (i.e., algorithm #6) to narrate the mathematical equations innatural language in accordance with one embodiment is depicted. At 802,the method may get the Mathematical Result TR 712 (output from algorithm#5 (FIG. 7)) containing the final values of all variables required bythe query to be answered.

Then at 804, the method may replace the variables in the mathematicalresult TR with the mapped words (subject(s) or (object(s) as per theoriginal mapping stored in Transient (Repository #1) 614. As previouslydescribed, the Transient Repository #1 may include the mapping ofsubject or objects to variable names (for a given set of sentences Sx).

Next at 806, the method may replace the operators in the mathematicalresult TR with equivalent verbs, numerals, or coefficients based on alookup of the proposed Dictionary #1 (114). As previously described, theDictionary #1 may map verbs and math operators.

Then at 808, morphological analysis and correction may be performed. Aspreviously explained, morphology is the identification, analysis anddescription of the structure of a given language's morphemes and otherlinguistic units, such as root words, affixes, parts of speech,intonation or stress, or implied context. According to oneimplementation of the present embodiment, the morphological analysis andcorrection may be performed by referring to the Dictionary #2 (526)which is the language dictionary and thesaurus repository.

Next at 810, the method may resolve anaphora. As explained above, ananaphora is a type of expression whose reference depends upon anotherreferential element. Then at 812, the method may perform disambiguation.As previously described, when a reader can reasonably interpret the samesentence as having more than one possible structure, the text isequivocal and meets the definition of syntactic ambiguity.

Next at 814, numerals are converted into numerical text. For example,the method may convert a numeral, such as “2” into numerical text, suchas “two”. Then at 816, the method may perform any other grammatical orsemantic corrections. Next at 818, the method may determine the finalnatural language sentence(s) as the answer to the original query.

FIGS. 9A-9B illustrate examples solving a math problem 900 using thedescribed algorithms in FIGS. 3-8 in accordance with one embodiment isdepicted.

Problem Statement: Ashish had 2 apples. He gave one to Joy. How many areleft?

Step #1 (904): Use algorithm #1 (FIG. 3) to get the input problemstatement (“Ashish had 2 apples. He gave one to Joy. How many areleft?”).

Step #2 (906): Use algorithm #1 (FIG. 3) to determine if the query isthe last sentence in the sequence (Result: YES).

Step #3 (908): Use algorithm #2 (FIG. 4) to check if the input sentencesare well-formed from a mathematical perspective (Result: NO).

Step #4 (910): Use algorithm #3 (FIG. 5) to convert source sentences towell-formed sentences from a mathematical perspective as per Sub-Steps 1thru 9 (902).

Output from Step #4 (910): Well-formed sentences (“Ashish had 2 apples.Ashish gave 1 apple to Joy. How many apples are left with Ashish?”).

Step #5 (912): Use algorithm #4 (FIG. 6) to get the input well-formedsentences (“Ashish had 2 apples. Ashish gave 1 apple to Joy. How manyapples are left with Ashish?”).

Step #6 (914): Use algorithm #4 (FIG. 6) to perform POS tagging, parsetree generation and determining typed dependencies for the inputsentences.

Step #7 (916): Use algorithm #4 (FIG. 6) to determine variables forsubject(s), object(s), verb(s), numeral(s), etc. from the typeddependencies.

Step #8 (918): Use algorithm #4 (FIG. 6) to lookup proposed dictionary#1 to determine verb-operator mapping.

Step #9 (920): Use algorithm #4 (FIG. 6) to construct the relevantequations for the sentences (except for the actual question to beanswered).

Output from Step #9 (920): Set of mathematical equations to be solved.

Step #10 (922): Use algorithm #5 (FIG. 7) to get the set of allmathematical equations (“input equations”) for the given set ofsentences (Sx).(Original Equation #1) NSUBJ1=2*DOBJ1(Original Equation #2) NSUBJ1=NSUBJ1−1*DOBJ1(Original Equation #3) POBJ1=POBJ1+1*DOBJ1

Step #11 (924): Use algorithm #5 (FIG. 7) to solve or resolve the set of“input equations” to a final set of equations (“target equations”) Tx,such that each of the target equations is unique and exclusive fromother target equations in the set Tx and the set of equations Tx cannotbe resolved further in terms of its constituent variables.(Original Equation #1) NSUBJ1=2*DOBJ1(Substitute value of NSUBJ1 from Equation #1 into Equation #2)NSUBJ1=2*DOBJ1−1*DOBJ1(Final Equation #2) NSUBJ1=1*DOBJ1(Initialize value of POBJ1) POBJ1=0(Substitute initial value of POBJ1 into Equation #3) POBJ1=0+1*DOBJ1(Final Equation #3)POBJ1=1*DOBJ1

Step #12 (926): Use algorithm #5 (FIG. 7) to determine the variablespresent in the original question to be answered. From Step #7, it isdetermined that the Question (Math Problem) needs to be answered/solvedin terms of NSUBJ1 and DOBJ1.

Step #13 (928): Using algorithm #5 (FIG. 7), from Step #11 and Step #12above, it is determined that the final equation #2 gives the solution interms of NSUBJ1 and DOBJ1, and is the mathematical result TR.(Mathematical Result TR) NSUBJ1=1*DOBJ1

Step #14 (930): Using algorithm #6, (FIG. 8) for the mathematical resultTR, replace the variables with the mapped words (subject(s)/object(s))to obtain the final mathematical result:(Result TR) NSUBJ1=1*DOBJ1(Replaced variables with mapped words) Ashish=1*Apples

Step #15 (932): Using algorithm #6 (FIG. 8), replace the operators inthe mathematical result TR with equivalent verbs/numerals/coefficients,based on a lookup of the proposed dictionary #1:(Replaced operators “=” with “has” and “*” with <blank>) Ashish has 1Apples

Step #16 (934): Using algorithm #6 (FIG. 8), perform morphologicalanalysis, anaphora resolution, structural disambiguation and any othergrammatical corrections as required to get the final answer to theoriginal query:(Morphological analysis+any other corrections to get final answer)Ashish has 1 apple left.

FIG. 10 is a block diagram 1000 of internal and external components ofcomputers depicted in FIG. 1 in accordance with an illustrativeembodiment of the present invention. It should be appreciated that FIG.10 provides only an illustration of one implementation and does notimply any limitations with regard to the environments in which differentembodiments may be implemented. Many modifications to the depictedenvironments may be made based on design and implementationrequirements.

Data processing system 800, 900 is representative of any electronicdevice capable of executing machine-readable program instructions. Dataprocessing system 800, 900 may be representative of a smart phone, acomputer system, PDA, or other electronic devices. Examples of computingsystems, environments, and/or configurations that may represented bydata processing system 800, 900 include, but are not limited to,personal computer systems, server computer systems, thin clients, thickclients, hand-held or laptop devices, multiprocessor systems,microprocessor-based systems, network PCs, minicomputer systems, anddistributed cloud computing environments that include any of the abovesystems or devices.

User client computer 102 (FIG. 1), and network server 112 (FIG. 1) mayinclude respective sets of internal components 800 a, b and externalcomponents 900 a, b illustrated in FIG. 10 Each of the sets of internalcomponents 800 a, b includes one or more processors 820, one or morecomputer-readable RAMs 822 and one or more computer-readable ROMs 824 onone or more buses 826, and one or more operating systems 828 and one ormore computer-readable tangible storage devices 830. The one or moreoperating systems 828 and Arithmetic and Algebraic Problem SolvingProgram 108A (FIG. 1) in client computer 102 (FIG. 1) and Arithmetic andAlgebraic Problem Solving Program 108B (FIG. 1) in network servercomputer 112 (FIG. 1) are stored on one or more of the respectivecomputer-readable tangible storage devices 830 for execution by one ormore of the respective processors 820 via one or more of the respectiveRAMs 822 (which typically include cache memory). In the embodimentillustrated in FIG. 10, each of the computer-readable tangible storagedevices 830 is a magnetic disk storage device of an internal hard drive.Alternatively, each of the computer-readable tangible storage devices830 is a semiconductor storage device such as ROM 824, EPROM, flashmemory or any other computer-readable tangible storage device that canstore a computer program and digital information.

Each set of internal components 800 a, b, also includes a R/W drive orinterface 832 to read from and write to one or more portablecomputer-readable tangible storage devices 936 such as a CD-ROM, DVD,memory stick, magnetic tape, magnetic disk, optical disk orsemiconductor storage device. A software program, such as Arithmetic andAlgebraic Problem Solving Program 108A and 108B (FIG. 1), can be storedon one or more of the respective portable computer-readable tangiblestorage devices 936, read via the respective R/W drive or interface 832and loaded into the respective hard drive 830.

Each set of internal components 800 a, b also includes network adaptersor interfaces 836 such as a TCP/IP adapter cards, wireless Wi-Fiinterface cards, or 3G or 4G wireless interface cards or other wired orwireless communication links. The Arithmetic and Algebraic ProblemSolving Program 108A (FIG. 1) in client computer 102 (FIG. 1) andArithmetic and Algebraic Problem Solving Program 108B (FIG. 1) innetwork server 112 (FIG. 1) can be downloaded to client computer 102(FIG. 1) from an external computer via a network (for example, theInternet, a local area network or other, wide area network) andrespective network adapters or interfaces 836. From the network adaptersor interfaces 836, the Arithmetic and Algebraic Problem Solving Program108A (FIG. 1) in client computer 102 (FIG. 1) and the Arithmetic andAlgebraic Problem Solving Program 108B (FIG. 1) in network servercomputer 112 (FIG. 1) are loaded into the respective hard drive 830. Thenetwork may comprise copper wires, optical fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers.

Each of the sets of external components 900 a, b can include a computerdisplay monitor 920, a keyboard 930, and a computer mouse 934. Externalcomponents 900 a, b can also include touch screens, virtual keyboards,touch pads, pointing devices, and other human interface devices. Each ofthe sets of internal components 800 a, b also includes device drivers840 to interface to computer display monitor 920, keyboard 930 andcomputer mouse 934. The device drivers 840, R/W drive or interface 832and network adapter or interface 836 comprise hardware and software(stored in storage device 830 and/or ROM 824).

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

What is claimed is:
 1. A processor-implemented method for solving andanswering an arithmetic or algebraic problem through a computer-basedquestion-answer system in real-time, using natural language processing(NLP) and an online dictionary, the method comprising: creating andmaintaining the online dictionary, wherein creating and maintaining theonline dictionary comprises: determining a relationship between at leastone verb and at least one math operator; mapping the at least one verbto at least one math operator based on the determined relationship;storing the mapped at least one verb to the at least one math operatorin the online dictionary; identifying an effect of the stored at leastone math operator on a plurality of subjects; identifying an effect ofthe stored at least one math operator on a plurality of objects;correlating the identified effect of the stored at least one mathoperator to the plurality of subjects; correlating the identified effectof the at least one math operator to the plurality of objects; updatingthe online dictionary with the correlated identified effect of the atleast one math operator to the plurality of subjects; and updating theonline dictionary with the correlated identified effect of the at leastone math operator to the plurality of objects; receiving, by a processorassociated with a first computer, an input statement, wherein the inputstatement is a geometric word problem that includes a plurality ofgeometric figures, angles, perimeters, and areas described by aplurality of words, entered by a user in natural language without amathematical operator symbol, via a user interface associated with acomputing system; determining whether each sentence within a pluralityof sentences associated with the input statement is a well-formedsentence from a mathematical perspective, wherein determining whethereach sentence within the plurality of sentences associated with theinput statement is a well-formed sentence from a mathematicalperspective comprises: performing part-of-speech (POS) tagging andparsing or parse tree generation on each sentence within the pluralityof sentences; and determining a typed dependency for each sentencewithin in the plurality of sentences and if each sentence within theplurality of sentences requires anaphora resolution; converting eachstatement into a well-formed sentence based on the determining whethereach sentence within a plurality of sentences associated with the inputstatement is a well-formed sentence from a mathematical perspective,wherein converting each statement into a well-formed sentence comprises:performing part-of-speech (POS) tagging and parsing or parse treegeneration on each sentence within the plurality of sentences; anddetermining if a plurality of user input is required to resolve aplurality of ambiguity associated with at least one sentence within theplurality of sentences; in response to determining the plurality of userinput is required to resolve the plurality of ambiguity, prompting theuser for the plurality of input to resolve the plurality of ambiguity;and in response to receiving the plurality of user input, performingstructural disambiguation for each sentence within the plurality ofsentences; converting each well-formed sentence into a mathematicalequation to form a set of equations, wherein forming the set ofequations comprises receiving the plurality of input entered by the userand storing each mathematical equation in an online repository, whereinthe converting the well-formed sentence into the mathematical equationand solving the set of equations comprises communicating online with asecond computer to access the online dictionary containing a mappingbetween a plurality of verbs, a plurality of action words, and aplurality of mathematical operators, wherein the dictionary is created,updated, and maintained separately on a server, and wherein thedictionary specifies for each verb within the plurality of verbs or eachaction word within the plurality of action words, the effect of theplurality of at least one mathematical operator within the plurality ofmathematical operators on an operand of a sentence and wherein theconverting the well-formed sentence into the mathematical equation andsolving the set of equations further comprises determining the effect ofthe plurality of at least one mathematical operator within the pluralityof mathematical operators on the operand of the sentence based onelectronically reading the dictionary and determining for each verbwithin the plurality of verbs or each action word within the pluralityof action words, the effect of the plurality of the at least onemathematical operator within the plurality of mathematical operators onthe operand of the sentence and performing a plurality ofonline-computing techniques, wherein the plurality of online computingtechniques comprises performing part-of-speech (POS) tagging, performingparsing or parse tree generation, determining a typed dependency, anddetermining a subject, an object, a verb, an action, and a numeral fromthe typed dependency; retrieving the formed set of equations from theonline repository; solving the retrieved set of equations to compute amathematical result; and narrating the mathematical result in naturallanguage, wherein the mathematical result is narrated as an automaticinteractive response or a solution from the computer system in real-timeand comprises converting the mathematical result into at least onenatural language sentence.
 2. The method of claim 1, wherein the solvingthe set of equations comprises a transient repository containingequations for a given set of sentences.
 3. The method of claim 1,wherein determining the typed dependencies comprises at least one ofdetermining whether the sentence requires at least one of an anaphoraresolution; a structural disambiguation; a morphological analysis; and aconversion of numerical text to a numeral.
 4. The method of claim 1,wherein performing morphological analysis and correction comprises adictionary containing a language dictionary and a thesaurus repository.5. The method of claim 1, wherein the determining a subject, an object,a verb, an action, and a numeral from the typed dependency comprises atransient repository containing a mapping of a subject or an object to avariable name.